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Archived threads in /sci/ - Science & Math - 1251. page

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A few years ago, I wrote a simple Fortran 2003 code to compute bandstructures using the empirical pseudopotential method, and which also has basic capabilities to also compute the density of states. https://github.com/aphirst/BandFTN

The algorithm constructs the matrix equation

[math]\mathbf{H} \mathbf{A} = E \mathbf{A}[/math]

for each k, where H depends on the wavevectors k, lattice vectors G, and pseudopotentials, solves for its eigenvalues and eigenvectors, and the eigenvalues are of course the values of the energy bands at each k, plot-able as a bandstructure if k is varied along the high symmetry directions.

The A vector is basically \psi but with the plane wave components factored out, as per:

[math]\psi_k(r) = e^{i k.r} u_k(r) \\
u_k(r) = \sum_{g'} a_{g'}(k) e^{i g'.r} \\
\psi_k(r) = \sum_{g'} a_{g'}(k) e^{i(k+g').r}[/math]

g and g' index the ordered list of Miller indices, for the potential and wavefunction expansions respectively.

The density of states is evaluated by computing the eigenvalues for a set of 'special' (symmetry reduced inside the Brillouin Zone) k-points (weighted according to their symmetry), and then Gaussian smearing to convert the discrete values into an approximate continuous curve.

So far, so good, but nothing has been done yet with the eigenvectors which are computed alongside the energy eigenvalues. Tons of literature states in a fairly superficial way that these eigenvectors can be used somehow in conjunction with Fourier Transformations to compute the charge density over the unit cell, however, I'm somewhat rusty on the topic, and my attempts to understand exactly what to do are instead getting confused by the lack of implementation-specific details and conflicting definitions of terms.

Is anyone able to point to me to a source they know to cover this in a clear, applicable way; or even better, explain themselves what exactly it is that needs to be done to generate such a charge density plot?
20 posts and 3 images submitted.
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>>8456291
This is about as far as I can get:

Each eigenvector for a given k will be a list of coefficients which can presumably be combined with the corresponding plane waves (from the ordered list of MIller indices, in increasing magnitude). You're probably supposed to perform this combination on a k-space grid, and then Fourier Transform this to a real space grid, though exactly what grids I'm supposed to generate (dimensions, spacings) and what /exactly/ to put in them escapes me.
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>>8456294
Oh, and of course, for the charge density it's going to be an integral over the k-points, i.e. a sum over the same special k-points used for the DoS calculations. Somehow.
>>
I found another source which appears to /almost/ describe what to do, but of course fails to enlighten me enough to know what to implement myself.

http://www.tcm.phy.cam.ac.uk/~mjr/castep/g-space.pdf

It talks about defining a reciprocal space grid (note that the coordinate values run from negative to positive, not from 0 upwards!), filling some of the points up to [math]g \leq G_{max}[/math] with their corresponding [math]\psi(g)[/math] (determined using the eigenvectors I think, though the exact evaluation is of course also omitted so I'm still not 100% sure what to ACTUALLY code...), filling up the rest of the space with 0s, defining an equivalently sized grid in "real" space (though not defining how these grid points actually relate to real space points), and then performing the discrete Fourier transform.

Aside the fact that I /still/ don't know exactly what values to be populating into this reciprocal space grid (help also appreciated there), I'm not sure this Fourier transform is as simple as they claim. All the literature I have on DFTs has the domains of the data defined with indices from 0 to N, and I'm fairly sure that you can't just shift your function and expect the Fourier transform to make sense.

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>Harvard researchers have studied and observed solid hydrogen under pressure at low temperatures. With increasing pressure we observe changes in the sample, going from transparent, to black, to a reflective metal, the latter studied at a pressure of 495 GPa. They have measured the reflectance as a function of wavelength in the visible spectrum finding values as high as 0.90 from the metallic hydrogen. They have fit the reflectance using a Drude free electron model to determine the plasma frequency of 30.1 eV at T= 5.5 K, with a corresponding electron carrier density of 6.7x10^23 particles/cm3 , consistent with theoretical estimates. The properties are those of a metal. Solid metallic hydrogen has been produced in the laboratory.

>* they have made some metallic hydrogen and have it in a cryostat in liquid nitrogen
>* they might leave it under pressure and let it warm to room temperature or they could keep it cold and release the pressure
>* they are planning to test for high temperature superconductivity

>If it stays a metal at room temperature and after releasing pressure and was also a superconductor then it would be the holy grail of physics.

https://arxiv.org/ftp/arxiv/papers/1610/1610.01634.pdf
http://www.nextbigfuture.com/2016/11/harvard-researchers-created-solid.html
54 posts and 6 images submitted.
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Hory shit

>496 Giga Pascals

Op you loaned your mom for this project?
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>>8456023
>If it stays a metal at room temperature and after releasing pressure and was also a superconductor then it would be the holy grail of physics.

If I could stay a metal at room temperature and after releasing pressure and was also a superconductor then I would be the holy grail of physics
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>>8456093
same thing desu

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>A striking feature of modern science is the disproportion between practical intelligence and intelligence as such: a scientist may be capable of the most extraordinary calculations and achievements but may at the same time be incapable of understanding the ultimate causality of things; this amounts to an illegitimate and monstrous disproportion, for the man who is intelligent enough to grasp nature in its deepest physical aspects, ought also to know that nature has a metaphysical Cause which transcends it, and that this Cause does not confine itself to determining the laws of sensory existence, as Spinoza claimed. What we have called the 'inhuman' character of modern science also appears in the monstrous fruits it produces, such as the overpopulation of the globe, the degeneration of humankind, and, by compensation, the means of mass destruction.

how do you respond?
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>>8455973
>tfw to intelligent to be incapable of understanding the ultimate causality of things; this amounts to an illegitimate and monstrous disproportion, for the man who is intelligent enough to grasp nature in its deepest physical aspects, ought also to know that nature has a metaphysical Cause which transcends it, and that this Cause does not confine itself to determining the laws of sensory existence, as Spinoza claimed. What we have called the 'inhuman' character of modern science also appears in the monstrous fruits it produces, such as the overpopulation of the globe, the degeneration of humankind, and, by compensation, the means of mass destruction.
>>
>>8455973
>how do you respond?

You can't blame science for psychological or germline warfare tactics.

The other part of your statement where you seem to be suggesting a transcendant external cause to the universe doesn't really require a response, since it is nessecarily outside the perview of sceintific observation, and thus science cannot say anything about it, for good or ill.
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>>8455973
>but may at the same time be incapable of understanding the ultimate causality of things
You're confusing your shitty baseless beliefs for "intelligence" and proclaiming that not believing your shitty baseless beliefs is a flaw.

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how is gravity even real? i mean it requires zero effort for some smaller object to move to a specific way just because of this "gravity" meme and some bigger object like a planet simply being big
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Welcome to the most fundamental question of physics, debated since the days of Aristotle. The reason I liked Einstein's explanation is because it managed to sidestep the issue entirely. I'm a lot more willing to swallow nonsense like curved spacetime than live in a world that allows action at a distance.
>>
Really, she's got so much metamusil in her closet. I was like, 'damn' when I saw it.
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>>8461098
how is electromagnetism even real? i mean it requires zero effort for some positively charged object to move to a specific way just because of this "electromagnetism meme" meme and some negatively charged object like a planet simply being negatively charged

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What does /sci/ think about mind control?
https://www.google.com/patents/US6506148
6 posts and 1 images submitted.
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You exercise mind control every day when you refrain from masturbating in public.
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>>8460910
i must not be very good at mind control then.
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>>8460910
Ya don't control your mind, you are your mind ya dingus

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What letter is this /sci/?
I cannot figure it out for the life of me.
I've narrowed it down to maybe:
https://en.wikipedia.org/wiki/Ze_(Cyrillic)
OR
https://en.wikipedia.org/wiki/Abkhazian_Dze
7 posts and 1 images submitted.
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>>8460822
>Ze
That's my pronoun you fucking shitlord
>>
>>8460822
definitely not "З"
Maybe just "\mathfrak{I}": [math]\mathfrak{I}[/math] in some different font
>>
>>8460832
THANK YOU!
I had been trying to find that for a very long time.

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If you're so smart then tell me what the fuck he meant by this
8 posts and 1 images submitted.
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>>8460795
Where there is smoke, there is fire
>>
>>8460795
Beta orbiters orbit cause they expect nudes.
>>
>>8460795
An apple a day keeps the doctor away

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Any of you guys have tips for better understanding math? I've always struggled with it but would like to improve. I'm majoring in biology so i only have to get through calculus.
10 posts and 2 images submitted.
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>>8460748
Stop being a brainlet
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>>8460773
but how?
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>>8460748
>so i only have to get through calculus.

The hardest part of calculus is algebra. More than likely your algebra is severely lacking. Learn it again and cement it. Everything from trig to exponents to etc...

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i'm dumb as fuck, ok? and i have an exam right now, since this one and s4s are the only intelligent 4chan forums, i came here searching for help
you respond and i will keep posting problems
32 posts and 6 images submitted.
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>>8460687
This is a very interesting number. It is the smallest number that can be written as the sum of the reciprocals of two consecutive even integers in two different ways.
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>>8460695
and... what do that means?
>>
Play around with any even number and it's inverse/reciprocal is just one over whatever number. The two consecutive even integers part of the problem a huge help with just straight out playing with numbers.

It's 10 and 12.

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Whatever you eat, your body processes it and strips all the nutrients from it until nothing but the components that make up shit are left. How does the body know what exactly to remove from every digestible material that is ingested, to make it so that nothing but shit components remain? Keep in mind that the body does this for whatever you eat, no matter if no human has ever eaten it before.

Dare I say, atheists fucking BTFO?
7 posts and 1 images submitted.
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>>8460530
>frog
>retarded post

Everytime.
>>
>>8460530
>How does the body know what exactly to remove from every digestible material that is ingested
it doesn't. It simply follows the same process every time, and it happens to work for some things. For example, say I gave you a sledge hammer and told you to break down everything in a house. Since you're a retard, you would just wack everything with the sledge hammer til you got tired. Some things would be broken down, other things would not. You wouldn't specifically target things that could be smashed and your body doesn't specifically target nutrients, or poisons wouldn't kill you. It's just like a retard randomly smashing on things or another retard randomly making troll posts on /sci/ and seeing what breaks.
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>>8460553
what kind of analogy is this? the basic concept is that each part of your digestive system basically dissolves what you eat to simpler parts, and then if your intestines can actually absorb it goes into your bloodstream, otherwise it's shit.

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were ancient Egyptians capable of any notion of calculus?
11 posts and 1 images submitted.
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>>8460486
It wasnt deductive, but hell yes. Newton put it all together sure, but the pieces existed for thousands of years.
>>
>>8460486

No. The answer is no.

t. wrote almost all of the wiki on pic related
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>>8460497
the moscow papyrus shows they were able to derive the formula for a frustum which relies on modern calculus.

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This is a serious scientific question
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>>8460394
Nothing i think since they have that ball

And what are these btw?
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>>8460394
I don't know. Do you have electrostatic charge stored in your piss?
>>
>>8460402
no but can't the salt in urine cause conduction?

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Can someone please explain to me why they find their particular field fascinating?

I've always grown up in an environment where it's a given fact that any academic pursuit is inherently boring. My college courses certainly aren't changing my mind. I thought that the field I'm going into was very interesting, but college seems to be trying to beat that out of me.
12 posts and 1 images submitted.
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you assume that everyone finds their particular field fascinating
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>>8460098
:D
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>>8460098
Why else would you waste your time in academia? You'd be better off doing literally anything else.

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Just how do you learn this?

How do I force myself to like it? Reading the material, the manufacturing processes and their results feels like reading a cooking recipe.

I end up questioning whats the point of reading this, what is there to do with this information I am collecting if I am not going to really do any of this stuff.

Please guide this brainlet, tell me how do I get the most out of this?
14 posts and 2 images submitted.
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>>8459942
>studying something you don't naturally enjoy
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>>8459965

Its an obligatory course I will have to repeat because of the very same reasons.

I might not naturally enjoy it, but I have to. Besides I do have SOME interest in learning it because I know there has to be something in there that perhaps could give me a better insight on other things.
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>>>8459978
If it is an obligatory course then it is a core part of your major.

You picked the wrong major.

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>What are you studying/have studied?

>What do you like the most about it?

>What are you finding difficult?

Also question to Americans, cam you explain this majoring and minor thing to me?

Here in Ireland, well my course in particular, we've got set modules throughout the bachelors degree. I can't pick and choose or drop anything.
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>>8459347
>Here in Ireland, well my course in particular
it seems to me that you use the word "course" the way we'd use the word "major". A minor is basically like choosing another subject to major in but not completing every single requirement needed.

t. physics major
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>>8459347
Major is your field of study, minor is usually a specialisation or an add on of another field.
There is a core curriculum of classes that are compulsory for your major and minor, then the rest are electives, however if you do a minor then usually it decreases the number of electives you can take (because it replaces them)


I'm doing biomedical science
I like immunology the most
I find the compulsory English classes boring, so I don't do as well in them
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>>8459347

>Physics

>Hopefully I will die soon

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